This paper studies the efficiency of equilibria in a productive OLG economy where the process of financial intermediation is characterized by costly state verification. Both competitive equilibria and Constrained Pareto Optimal allocations are characterized. It is shown that market outcomes can be socially inefficient, even when a weaker notion than Pareto optimality is considered.Financial intermediation, costly state verification, Constrained Pareto Optimality

Giorgio Di Giorgio

English

Research Papers in Economics

Financial Intermediation and Equity Investment with
Costly Monitoring
Giorgio Di Giorgio*
Università degli Studi di Roma “La Sapienza”
and Università “Luiss Guido Carli”
September 1999
Abstract:  This paper studies the efficiency of equilibria in a productive OLG
economy where the process of financial intermediation is characterized by costly state
verification.  Both competitive equilibria and Constrained Pareto Optimal allocations are
characterized. It is shown that market outcomes can be socially inefficient, even when a
weaker notion than Pareto optimality is considered.
Keywords:  Financial Intermediation, Costly State Verification, Constrained Pareto
Optimality.
J.E.L. Classification Numbers:  E44, E62.
                                               
*Correspondence: Giorgio Di Giorgio, Dipartimento di Economia Pubblica, Università La Sapienza di Roma,
Via del Castro Laurenziano 9, 00161, Roma, Italy.  Tel. 39-06 4976 6362,  Fax: 39-06-4461964.
Email: digiorg@dep.eco.uniroma1.it2
Financial Intermediation and Equity Investment with Costly Monitoring°
1. Introduction
As is well known, competitive equilibria of OLG economies may be inefficient even when
markets are complete.  The competitive equilibrium of a productive economy may not be
Pareto optimal because of overaccumulation of capital (Diamond, 1965):  in dynamically
inefficient economies, the introduction of either a tax-transfer scheme, as a pay as you go
social security system, or public debt allows for an increase of welfare.
When uncertainty and market incompleteness are present in the economy,
intergenerational transfer policies have also the role of providing risk sharing services.
Young agents invest in a risky productive activity to be able to consume when old.  In
absence of a mutual fund, social security or public debt provide a risk-free way to transfer
wealth over time. The same task could as well be undertaken by financial intermediaries,
which collect deposits and lend to a large number of firms, thereby perfectly diversifying risk.
This paper studies the efficiency of equilibria in a productive OLG economy with
asymmetric information.  The model draws on Reichlin and Siconolfi (1996): consumers
allocate their disposable wealth between equity shares and (bank) deposits, and firms have
access to a random technology, whose input can be financed either by selling shares to
consumers or by loans.  However, while Reichlin and Siconolfi (1996) consider the effects of
adverse selection,1 here the economy is affected by ex-post moral hazard due to costly state
verification: output is freely observable only by firms, while lenders have to pay some
monitoring costs to observe its realization (Townsend, 1979; Williamson, 1987). As in
Diamond (1984), costly state verification would allow to derive endogenously the existence of
                                               
° This paper is based on the first chapter of my Ph.D. Dissertation at Columbia University, New York.   I am
strongly indebted with Paolo Siconolfi and Pietro Reichlin for many long and precious discussions on this work.
I also thank Edmund Phelps, Glenn Hubbard, Roberto Perotti, Nicola Cetorelli and Phillip Jefferson for their
useful comments.  Financial support from CNR is also gratefully aknowledged.  Obviously, I am the only one
responsible for any remaining mistakes.
1 See also Azariadis and Smith, 1993.3
financial intermediaries (banks) acting in the economy as delegated monitors of lenders.
However, we simply assume that direct lending is not available, and that firms can only
borrow from banks.  As a result, the cost of monitoring affects the deposits interest rate,
which in the model is strictly less than the expected return on shares.
In this framework, the introduction of a tax-transfer scheme (e.g. social security) by
the government may be welfare improving even when the economy is dynamically efficient:
in fact, when monitoring is too costly, the government could establish a pay as you go social
security system (or issue public debt) in order to replace the risk-sharing activity provided by
financial intermediaries. The reason for this result is that, in a market economy, social security
and bank deposits develop essentially the same role. A benevolent government should decide
to use only the instrument whose returns allow for higher consumption opportunities.
Although the economy is affected by asymmetric information and market
incompleteness, the inefficiency of competitive equilibria might also be related to additional
factors.  To analyze these effects, we define a notion of constrained Pareto optimality, that
assumes that market incompleteness cannot be eliminated and that the planner is subject to the
same information structure of the individuals in the market economy.  We show that, in the
case of a productive economy, the Constrained Pareto Optimum and the competitive
equilibrium are characterized by different allocations of the instruments. The reason is that
banks' profit maximizing behaviour is privately efficient, but socially inefficient.  In
particular, competitive banks' best response to firms declaring bankruptcy is to adopt
stochastic verification procedures and a severe punishment for dishonest firms. However, the
planner internalizes the fact that firms are owned by consumers and act in the interest of the
latter.  From a social point of view, it is never optimal to punish firms too harshly.  At a
Constrained Pareto Optimum,  firms are subject to deterministic monitoring when they
declare bankruptcy, but the optimal level of punishment is lower than the one chosen by
competitive banks.  Financial intermediation provided by profit maximizing banks is then
responsible for the inefficient outcome of the competitive equilibria.4
The paper is organized as follows.  In section 2, we present the model and describe the
partial equilibrium financing game played between representative firms and banks. Section 3
deals with general equilibrium and optimal government policies, while Constrained Pareto
Optimality is the object of section 4. Conclusions follow.
2. The model
2.1 Agents.
We study the stationary states of a simple general equilibrium OLG model in which
consumers, firms, banks and the government are present.  There is a continuum of identical
consumers, uniformly distributed on the [0,1] interval. They live for two periods, and
population is assumed to be stationary.  Each consumer is endowed with W units of a non
storable physical good when young, but she likes to consume only when old.  When young,
consumers are taxed by an amount T˛[ ] 0,W  chosen by the government, who transfers the
revenues to currently old people.  In the first period of their lives, consumers face only a
portfolio problem:  they have to choose how to allocate their after-tax endowment (W-T) in
two existing assets; more precisely, consumers can buy equity shares by endowing firms with
some amount of capital K, or they can buy deposits (D) supplied by financial intermediaries
(banks). Equity shares pay a state contingent rate of return, which depends on the outcome of
production.  We make the following simplifying assumption:
Assumption 1:  Each consumer can directly invest in equities of only one firm.2
A continuum of ex-ante identical firms is uniformly distributed on the [0,1] interval.
Each firm starts with no endowment but has access to a stochastic linear technology such that
                                               
2 This assumption rules out the possibility for our consumers to diversify their equity holdings.  It is an extreme
version of a capital market imperfection which prevents consumers to enter an ideal mutual fund able to
completely diversify its portfolio (See Reichlin and Siconolfi, 1996).5
X units of capital input return  aX  units of output  (a >1) with probability q, and  0  with
probability 1-q.  Investment returns are i.i.d. across firms.  When firms are endowed with K
units of capital from households (K is then the amount of stocks acquired), they can borrow  L
= X - K from banks.  Let R be the gross rate of interest that firms have to pay back when
production is positive;  with probability (1-q), instead,  the firm goes bankrupt and nothing is
due to the bank.
There is a finite number of competitive banks.  These are assumed not to be able to
buy stocks.  Banks collect deposits from households and are the only agents in the economy
able to perfectly diversify their portfolio by lending to a large number of firms;  for this
reason, the law of large numbers guarantees that bank deposits are a safe asset returning a
fixed interest rate to consumers.
The economy is characterized by ex-post moral hazard, as banks can observe the
realization of the investment process only if they accept to pay a monitoring cost, indicated
with letter g and assumed proportional to the loan amount.  The lending conditions of the
financial contract between banks and firms are studied in the next subsection.
2.2 The financing game.
Consider the game between a representative firm and a representative bank.  The firm
demands a loan, whose cost is set by the bank, and activates its production technology.  The
outcome of production is private information of the firm; the latter decides whether to report it
truthfully to the bank or lie (cheat).  The bank receives the report.  If the investment project is
reported to have been successful, the loan is repaid and the game ends.  Instead, if the firm
declares bankruptcy, the bank has to choose whether to trust the report, or pay the monitoring
cost and obtain full knowledge of the investment outcome. Both players are assumed to be
able to randomize on their available pure strategies. We will look for a Nash equilibrium of6
this game, where each player chooses his optimal strategy in order to maximize his expected
profits, given the opponent's choice.3
In a Nash equilibrium, banks will adopt a monitoring strategy.  Otherwise firms have
an incentive to report the realization of the "bad state" independently of the effective outcome
of production.  We will show that, as in Bernanke and Gertler (1989), the optimal monitoring
strategy of the banks involves stochastic verification procedures, that is banks monitoring
firms declaring bankruptcy with probability less than 1.  In order to prove this, it is sufficient
to show that a deterministic monitoring strategy can never be part of a Nash equilibrium of
this game. The argument runs as follows. Observe that firms never have an incentive to
misreport the outcome of production if banks play their proposed (deterministic) equilibrium
strategy, as they will always be monitored.  Then, firms never misreport.  Now, it is obvious
that banks are not playing a best response to the proposed equilibrium strategy of the firms,
because when they costly monitor reports announcing bad outcomes there is nothing left to
recover.  Hence, deterministic monitoring is not optimal,4 and the financing game does not
have any pure-strategy Nash equilibrium.  However, the game has a finite number of players
and the set of available strategies is finite: this implies that a Nash equilibrium does always
exist if one allows for mixed strategies.   Let  m  and  p  be respectively the probability that a
firm cheats by reporting the bad state when a positive outcome is realized, and the probability
                                               
3 Analogously, we could derive the corresponding optimal financial contract by simply applying the Revelation
Principle, as in Bernanke and Gertler (1989).  This would not change the analysis relevantly, except for the fact
that in equilibrium firms will never misreport (this is actually a further assumption: firms are assumed not to
misreport whenever they are indifferent between doing this or not). However, in reality, sometime firms do
misreport; the formalization in the text takes into account such a possibility.
4 This is a standard result that can be traced back to Townsend (1979), who pointed out that "stochastic
verification procedures can dominate deterministic procedures".  Moreover, sometimes stochastic monitoring is
also observed in the real world.  In Townsend's words: "Stochastic verification procedures are not uncommon.
The timing of bank audits by government agencies is somewhat random. Similarly corporations use stochastic
procedures in monitoring internal divisions, and it is also said that tax audits by the IRS are determined in part at
random."13
individual level: in this second case, once market incompleteness is eliminated, equilibria turn
out to be Pareto optimal.
When economies are also subject to asymmetric information, the inefficiency of
market clearing allocations is usually related to the agents' behaviour in a way which can be
distinguished from market incompleteness (Azariadis and Smith, 1993). Hence, even by
assuming that market incompleteness cannot be removed, one could try to establish whether
market equilibria satisfy a weaker notion of efficiency than Pareto optimality. This notion will
be called Constrained Pareto Optimality, and it is derived under the assumption that the
planner cannot introduce additional assets and is subject to the same information structure of
the individuals. Therefore, we give the following
Definition  A Constrained Pareto Optimum is an allocation (K,D,T) such that the expected
utility of the representative consumer is maximized, subject to the resource allocation
constraint, individual budget constraints, and the informative constraint that the planner
cannot freely observe outcomes of production activity.
Notice that when aq £ 1, the Pareto efficient allocation (and a fortiori the Constrained
Pareto Optimum) is trivially T* = W, which corresponds to the optimal policy in the market
economy.  Henceforth, we limit our attention to dynamically efficient economies where aq >
1.  The social planner can try to achieve his or her target by controlling the portfolio
allocation (K,D,T), the supply of loans (L), the interest rates on loans and deposits (R,I), the
punishment to the firm when this is caught cheating (V), and the probability (p) of monitoring
when bad outcomes are reported.  Moreover, contrary to the representative consumer, the
planner internalizes the effect of his (her) savings and monitoring choices on the assets'
returns.  The planner's problem can then be written as follows:17
bankruptcy with probability less than one, and they punish cheating by setting V = a(K+L).
However, firms are owned by consumers and act in their interest.  From the consumers' point
of view, deterministic monitoring dominates any stochastic verification procedure, while for
the banks only the latter is supported by profit maximization. This affects the returns offered
by the assets and the incentives to choose the optimal portfolio allocation. The banks' profit
maximizing behaviour is then responsible for the inefficient outcome of the competitive
equilibria.
Remark 2  Even though, when monitoring is not too costly, market outcomes and the
Constrained Pareto Optimum are both characterized by the active use of the same instruments
(L and K),  the equilibrium allocations are different.  Moreover, there is no optimal policy in a
market economy which can induce banks to monitor with probability equal to one when
bankruptcy is declared. Hence, this kind of market equilibria inefficiency cannot be
eliminated by using traditional macreoconomic policies.  In order to restore the efficient
outcome, the policymaker should act as a regulator of the microstructure of private
contracts.13
5. Conclusions.
This paper investigates the efficiency properties of a productive OLG model subject to ex-
post moral hazard in the form of costly state verification. Competitive equilibria are
characterized by banks adopting stochastic monitoring of bankruptcy reports, and firms
having an incentive to lie.  The optimal policy of the government introduces a social security
system under more general conditions than in the perfect information case.   We show that
market outcomes can fail to achieve even a weaker notion of efficiency than Pareto
optimality, which is derived under the hypothesis that market incompleteness cannot be
eliminated.  This result depends on the role of profit maximizing financial intermediaries:
                                               
13 In our example, the policy maker should require the lending contract  to be designed so as to include
deterministic monitoring of bankruptcy reports.18
these adopt stochastic verification procedures which are privately optimal, but socially
inefficient in an economy with private ownership.
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Financial intermediation and equity investment with costly monitoring

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